The set {a0,a1,…,an} of real numbers satisfies the following conditions:
(i) a_0 \equal{} a_n \equal{} 0,
(ii) for 1 \leq k \leq n \minus{} 1, a_k \equal{} c \plus{} \sum^{n\minus{}1}_{i\equal{}k} a_{i\minus{}k} \cdot \left(a_i \plus{} a_{i\plus{}1} \right)
Prove that c≤4n1. algebraSequencerecurrence relationInequalityIMO Shortlist